IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Alternative solutions of the black-sholes equation

  • Hortensia Fontanals Albiol
  • Ramon Lacayo
  • Josep Vives

    (Universitat de Barcelona)

Registered author(s):

    In the mathematical treatment of financial derivatives, and specially that of options, the defining stochastic differential equation coupled with the arbitrage-free pricing condition leads to a deterministic partial differential equation. The solution of this equation under appropriate boundary conditions is interpreted as the price of the asset. A review of the specialized financial literature reveals that, by and large, there are three main altrernative approaches to finding the function that describes the price of the contingent claim. Fist, we have the classical methods of solution of partial differential equations. These methods are widely used in phusics, but they have yet to take root in the economic arena. Their importance, however, cannot be overlooked, and we note in passing that even in the simplest cases the solution of a partial differential equation is everthing but trivial. A second approach can be found in the mehods of mathematical statistics, where the stochastic differential equation describing the asset price is solved via the equivalence between the financial no-arbitrage condition and that of a martingale. Both of these approaches often lead to closed-form solutions that are easy to use and convenient for the valuation of assets in real time. Finally, when a solution in closed form is not available or possible, numerical methods may provide an alternative solution. Nevertheless, the application of these methods in finance still presents great practical difficulties, due mainly to the time involved in obtaining a solution. This paper deals with the first of the approaches mentioned above. Using the Black-Scholes equation for the valuation of european options, a fairly detailed and simple description is given of some of the methods that can be used to solve this type of equation.

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below under "Related research" whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 58.

    as
    in new window

    Length: 0 pages
    Date of creation: 1999
    Date of revision:
    Handle: RePEc:bar:bedcje:199958
    Contact details of provider: Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
    Web page: http://www.ere.ub.es

    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:bar:bedcje:199958. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Espai de Recerca en Economia)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.